We prove that an isoperimetric region in R2 with density er must be convex and contain the origin, and provide numerical evidence that circles about the origin are isoperimetric, as predicted by the Log-Convex Density Conjecture.
Frank Morgan, Atwell Professor of Mathematics, Williams College
Chung, Ping Ngai; Fernandez, Miguel A.; Shah, Niralle; and Vieira, Luis Sordo
"Are circles isoperimetric in the plane with density er?,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16
, Article 12.
Available at: http://scholar.rose-hulman.edu/rhumj/vol16/iss1/12